[  [[1], [1, 1], [1]]      -1     1]
                      [                                  ]
                      [   [[1], [2], [1]]        -1     0]
                      [                                  ]
                      [ [[1], [1, 1, 1], []]     -1     3]
                      [                                  ]
                      [  [[1], [1, 2], []]       -1     2]
                      [                                  ]
                      [    [[1], [3], []]        -1     1]
                      [                                  ]
                      [  [[2], [], [1, 1]]       -1    -2]
                      [                                  ]
                      [    [[2], [], [2]]        -1    -1]
                      [                                  ]
                      [   [[2], [1], [1]]        -1     0]
                      [                                  ]
                      [  [[2], [1, 1], []]       -1     2]
                      [                                  ]
                      [    [[2], [2], []]        -1     1]
                      [                                  ]
                      [  [[1, 2], [], [1]]        1    -1]
                      [                                  ]
                      [    [[3], [], [1]]        -1    -1]
                      [                                  ]
                      [  [[1, 2], [1], []]        1     1]
                      [                                  ]
                      [    [[3], [1], []]        -1     1]
                      [                                  ]
                      [   [[1, 3], [], []]        1     0]
                      [                                  ]
                      [    [[4], [], []]         -1     0]

> 
>  #Total weight of vector partitions of 4
> 
>  add(vpw(V[i]),i=1..nops(V));
                                       5
>  nops(V);
                                       41

> #There are 41 vector partitions of 4 with total weight 5
  #which is p(4).

> 
> 
>  # vector partitions of 4 with crank = 0 mod 5
> 
>  V0:=vecptnsC(4,0,5);
V0 := [[[], [1], [3]], [[], [1, 1], [1, 1]], [[], [2], [2]], [[], [3], [1]],

    [[1], [1], [2]], [[1], [2], [1]], [[2], [1], [1]], [[1, 3], [], []],

    [[4], [], []]]

>  nops(V0);
                                       9

>  add(vpw(V0[i]),i=1..nops(V0));
                                       1

> 
>  # There are 9 vector partitions of 4 with crank = 0 mod 5
>  # and total weight = 1.
> 
>  # vector partitions of 4 with crank = 1 mod 5